stratified ABC [One World ABC webinar]

The third episode of the One World ABC seminar (Season 1!) was kindly delivered by Umberto Picchini on Stratified sampling and bootstrapping for ABC which I already if briefly discussed after BayesComp 2020. Which sounds like a million years ago… His introduction on the importance of estimating the likelihood using a kernel, while 600% justified wrt his talk, made the One World ABC seminar sounds almost like groundhog day!  The central argument is in the computational gain brought by simulating a single θ dependent [expensive] dataset followed by [cheaper] bootstrap replicates. Which turns de fact into bootstrapping the summary statistics.

If I understand correctly, the post-stratification approach of Art Owen (2013?, I cannot find the reference) corrects a misrepresentation of mine. Indeed, defining a partition with unknown probability weights seemed to me to annihilate the appeal of stratification, because the Bernoulli variance of the estimated probabilities brought back the same variability as the mother estimator. But with bootstrap, this requires only two simulations, one for the weights and one for the target. And further allows for a larger ABC tolerance in fine. Free lunch?!

The speaker in two weeks (21 May or Ascension Thursday!) is my friend and co-author Gael Martin from Monash University, who will speak on Focused Bayesian prediction, at quite a late time down under..!

“Scientists find genetic mutation that makes woman feel no pain”

A frontpage title in The Guardian of yesterday led me to think this was yet another entry about the Brexit Mayhem. Explaining much of the current mess. After checking it appeared to be unrelated… although the patient’s name being Cameron makes one still wonder.

the cult of nonsense

Nothing has changed. Again… And again. And again. Groundhog May does it again.

sleeping beauty

Through X validated, W. Huber made me aware of this probability paradox [or para-paradox] of which I had never heard before. One of many guises of this paradox goes as follows:

Shahrazad is put to sleep on Sunday night. Depending on the hidden toss of a fair coin, she is awaken either once (Heads) or twice (Tails). After each awakening, she gets back to sleep and forget that awakening. When awakened, what should her probability of Heads be?

My first reaction is to argue that Shahrazad does not gain information between the time she goes to sleep when the coin is fair and the time(s) she is awaken, apart from being awaken, since she does not know how many times she has been awaken, so the probability of Heads remains ½. However, when thinking more about it on my bike ride to work, I thought of the problem as a decision theory or betting problem, which makes ⅓ the optimal answer.

I then read [if not the huge literature] a rather extensive analysis of the paradox by Ciweski, Kadane, Schervish, Seidenfeld, and Stern (CKS³), which concludes at roughly the same thing, namely that, when Monday is completely exchangeable with Tuesday, meaning that no event can bring any indication to Shahrazad of which day it is, the posterior probability of Heads does not change (Corollary 1) but that a fair betting strategy is p=1/3, with the somewhat confusing remark by CKS³ that this may differ from her credence. But then what is the point of the experiment? Or what is the meaning of credence? If Shahrazad is asked for an answer, there must be a utility or a penalty involved otherwise she could as well reply with a probability of p=-3.14 or p=10.56… This makes for another ill-defined aspect of the “paradox”.

Another remark about this ill-posed nature of the experiment is that, when imagining running an ABC experiment, I could only come with one where the fair coin is thrown (Heads or Tails) and a day (Monday or Tuesday) is chosen at random. Then every proposal (Heads or Tails) is accepted as an awakening, hence the posterior on Heads is the uniform prior. The same would not occurs if we consider the pair of awakenings under Tails as two occurrences of (p,E), but this does not sound (as) correct since Shahrazad only knows of one E: to paraphrase Jeffreys, this is an unobservable result that may have not occurred. (Or in other words, Bayesian learning is not possible on Groundhog Day!)

41ièmes Foulées de Malakoff [5k, 7⁰C, 18:40, 40th & 2nd V2]

[Warning: post of limited interest to most, about a local race I ran for another year!]

Once more, I managed to run my annual 5k in Malakof. And once again being (barely) there on the day of the race. Having landed a few hours earlier from Birmingham. Due to traffic and road closures, I arrived very later in Malakoff and could not warm up as usual, or even squeeze to the first rows on the starting line. Given those handicaps, I still managed in getting close to my best time of last year (18:40 vs. 18:36). I alas finished second in my V2 category, just a few meters behind the first V2 and definitely catching up on him! My INSEE Paris Club team won the company challenge for yet another year. Repeating a pattern of now many years.